Measurement of the Hydrogen1S-2STransition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock

We report on an absolute frequency measurement of the hydrogen $1S\ensuremath{-}2S$ two-photon transition in a cold atomic beam with an accuracy of 1.8 parts in ${10}^{14}$. Our experimental result of 2 466 061 413 187 103(46) Hz has been obtained by phase coherent comparison of the hydrogen transition frequency with an atomic cesium fountain clock. Both frequencies are linked with a comb of laser frequencies emitted by a mode locked laser.